Calculus volume stuff

posted by .

Find the volume of the solid obtained by rotating the region bounded
y = 16 x and y = 2 x^2 about y =0

Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0

Find the volume of the solid generated by rotating the region bounded by
y = \sin^2(x) and y = 0
between 0 and pi about the x-axis

  • Calculus volume stuff -

    washers: v=∫[0,8] π(R^2-r^2) dx
    where R=16x and r=2x^2
    = 2621454/15 π

    shells: v=∫[0,128] 2πrh dy
    where r=y and h=√(y/2)-y/16
    = 2621454/15 π

    Can you set up the other integrals?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus edit

    1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the …
  2. Calculus

    This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
  3. calculus

    Consider the solid obtained by rotating the region bounded by the given curves about the line x = 4. x= 4y^2 , x = 4 Find the volume V of this solid.
  4. CALCULUS 2

    Consider the solid obtained by rotating the region bounded by the given curves about the line x = 1. y = x, y = 0, x = 4, x = 6 Find the volume V of this solid
  5. calculus

    Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3 . Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0.
  6. calculus

    Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips would …
  7. calculus

    Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the …
  8. Calculus

    a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
  9. CALCULUS MAJOR HELP!!!!!!

    Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
  10. Calculus I don't understand

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …

More Similar Questions